How do I select parts of my model to independently rotate?
TL;DR
Turning your teeth can be somewhat painful, and the results can be ugly! You have been warned!
Summary:

Go into Edit Mode (Tab).
Make your selection somehow (C circle select, for instance).
separate the object (P).
Go back to Object Mode (Tab).
Move the origin to the center of mass (ShiftCtrlAltC)
Rotate somehow (RR for instance).
optional: fill the gaps.

Walk-through:
It's not going to be an easy job: 3D scans tend to be very messy and extremely dense in terms of vertex count! Also: teeth are usually very close to each other and they don't stand on a perfectly circular base area (so it's impossible to turn them without clashes). But you can try :)
This is a very poor attempt at making a set of teeth: say you want to move the second from the right.

Tab to the edit mode, then navigate (zoom in/out by turning the mouse wheel, turn around by pressing the mouse wheel, move around by holding Shift while pressing the mouse wheel) until you have your tooth &quot;aligned&quot; with the view (use Z to change to wireframe if needed). When you have it from the right point of view, hide all the rest from the view, by hitting AltB and making a rectangle.

Now select your tooth vertices with precision. Use C to enable a &quot;circle select&quot; (you control the size of the circle by scrolling the mouse wheel). Add new vertices, then click the right mouse button to exit the selection, then turn around, press C again, and so on. You can always CtrlZ to undo.

Bring the rest into view by using AltB again. Then hit P &gt; &quot;Selection&quot;. This will separate your tooth from the rest of the mesh. You can now exit edit mode: Tab.

Select your &quot;loose tooth&quot;, hit ShiftCtrlAltC &gt; &quot;Origin to center of mass&quot;. Then use RR to rotate: R then Z will help but only if your model is correctly aligned Z-up.

Unfortunately now there is a gap between the tooth and the underlying surface. Filling it is another level of complexity...
A very rough way would be: selecting both your objects (tooth and the rest of your jaw), CtrlJ to join them. Tab into edit mode. A to deselect all. ShiftCtrlAltM to select the boundaries of the two holes. Spacebar &gt; Bridge Edge Loops to fill the hole. The filling wil be very rough though: